Newton's Law of Cooling

Question

Outside temperature is −5₀C. The temperature of an iron plate is 25₀C and it is kept outside. How long will it take the temperature to fall below 0₀C. Round your answer to two decimal places in minutes.

Answer 1

Newton's Law of Cooling is: dT/dt = - k (T - T_env)

The Solution is: T(t) = T_env + (T₀ - T_env) e^-kt

Solving analytically,

(T(t) - T_env)/(T₀ - T_env) = e^-kt

t = (-1/k) ln [(T(t) - T_env)/(T₀ - T_env)]

For this problem: T₀ = 25°C, T_env = -5°C and T(t) = 0°C

∴ t = ln (6)/k,

where k is the cooling constant that depends on surface area, shape, texture and other factors. This value is required for a precise answer.